Well we have a loose continuity. Mario's continuity is more dependent on who the characters are rather than the events themselves.
For example saying "Mario and Luigi are brothers" is a solid canonical statement that cannot change from game to game. But saying "there's no air in space" is not something that will stay consistent with this type of canon. The laws of physics and science will change from game to game, but Mario and Luigi will still be brothers.
For example saying "Mario and Luigi are brothers" is a solid canonical statement that cannot change from game to game. But saying "there's no air in space" is not something that will stay consistent with this type of canon. The laws of physics and science will change from game to game, but Mario and Luigi will still be brothers.